AICME II abstracts

Modelling the spread of diseases in animal populations

Frequency-dependent incidence in STD models: portrayal of pair-based transmission and effects of illness on contact behaviour James O. Lloyd-Smith1 and Wayne M. Getz2 . We investigate the transmission process for sexually-transmitted diseases (STDs) in populations with rapid pairing dynamics. Such populations include non-pair-bonding animals and ‘core groups’ of humans with high sexual activity. STD epidemics are commonly modelled using frequencydependent incidence — we seek to clarify the relationship between this simple formulation and the complex, pair-based contact process that underlies STD transmission. We then consider the case when infected individuals exhibit altered pairing behaviour, due to reduced vigour, social barriers, or behaviour modification by the pathogen [1, 2]. We present a mechanistic derivation of the classical frequencydependent incidence from a pairing model, using a timescale approximation that holds when pairing processes occur much faster than epidemic processes [3]. This derivation provides a framework to test how accurately the classical model portrays pair-based transmission, by comparison with a full pair-formation/epidemic model. This accuracy depends strongly on the disease being studied: frequency-dependent formulations are more suitable for chronic, less-transmissible infections than for transient, highlytransmissible infections. Our results thus support earlier proposals to divide STDs into these two functional classes [4]. We then extend the derivation to include situations where illness influences pairing behaviour, for populations where the timescale approximation is reasonable. For four cases of increasing behavioural complexity,

Modelling the spread of diseases in animal populations

analytic expressions are presented for the generalized frequency-dependent incidence rate, basic reproductive number (R0 ), and steady-state prevalence (i∞ ) of an epidemic. The expression for R0 is identical for all cases, giving refined insights into determinants of invasibility of STDs. Potentially significant effects of infection-induced changes in contact behaviour are illustrated by simulating epidemics of bacterial and viral STDs. We discuss application of our results to STDs (in animals and humans) and other infectious diseases.

References [1] Loehle, C., 1995, Social barriers to pathogen transmission in wild animal populations, Ecology 76: 326-335. [2] Beckage, N.E., 1997, Parasites and pathogens: effects on host hormones and behavior, New York, Chapman & Hall. [3] Heesterbeek, J.A.P. & J.A.J. Metz, 1993, The saturating contact rate in marriage- and epidemic models, J Math Biol 31: 529-539. [4] Garnett, G.P., 2002, The geographical and temporal evolution of sexually transmitted disease epidemics, Sex Trans Inf 78: 114-119.

1 Biophysics Graduate Group, University of California, Berkeley, CA, 94720, USA (e-mail: [email protected] ). 2 Department of Environmental Science, Policy & Management, University of California, Berkeley, CA, 94720, USA (e-mail: [email protected]).

15-Llo-a

AICME II abstracts

15-Llo-b